Saved in:
Bibliographic Details
Main Authors: Lin, Ban, Romo, Mauricio
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.07109
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We study autoequivalences of $D^{b}Coh(X)$ associated to B-brane transport around loops in the stringy Kähler moduli of $X$. We consider the case of $X$ being certain resolutions of determinantal varieties embedded in $\mathbb{P}^{d}\times G(k,n)$. Such resolutions have been modeled, in general, by nonabelian gauged linear sigma models (GLSM). We use the GLSM construction to determine the window categories associated with B-brane transport between different geometric phases using the machinery of grade restriction rule and the hemisphere partition function. In the family of examples analyzed the monodromies around phase boundaries enjoy the interpretation as loop inside link complements. We exploit this interpretation to find a decomposition of autoequivalences into simpler spherical functors and we illustrate this in two examples of Calabi-Yau 3-folds $X$, modeled by an abelian and nonabelian GLSM respectively. In additon we also determine explicitly the action of the autoequivalences on the Grothendieck group $K(X)$ (or equivalently, B-brane charges).